temp gauge high and air blowing warm

I had the same issue. Did tons of research, took it to several shops with several different guesses and finally to GM. They told me it was the thermostat which I disagreed because it was mechanical and nothing from the thermostat is connected to the temp gauge. They explained it to me and it made perfect sense. If the thermostat is not working, the car will run too cold or too hot, too cold in my case. The computer is set for he car to run within a certain temperature range. If it does not, it will send a fault message, usually P0128 to the computer which will shut down the air conditions, set the temp gauge to C and make the fans run all the time. I had them change the thermostat and it fixed all the problems.

On a 2008 the air conditioner is getting hot cool hot cool them it fina3get cold

How do you check the reservoir? I read in the manual that’s where you put it in.